diff options
Diffstat (limited to 'python/analytics/black.py')
| -rw-r--r-- | python/analytics/black.py | 22 |
1 files changed, 15 insertions, 7 deletions
diff --git a/python/analytics/black.py b/python/analytics/black.py index ba9d8e96..94f91efb 100644 --- a/python/analytics/black.py +++ b/python/analytics/black.py @@ -3,13 +3,16 @@ from numba import jit, float64, boolean from scipy.stats import norm import math + def d1(F, K, sigma, T): return (log(F / K) + sigma**2 * T / 2) / (sigma * math.sqrt(T)) + def d2(F, K, sigma, T): return d1(F, K, sigma, T) - sigma * math.sqrt(T) -@jit(cache=True,nopython=True) + +@jit(cache=True, nopython=True) def d12(F, K, sigma, T): sigmaT = sigma * sqrt(T) d1 = log(F / K) / sigmaT @@ -18,27 +21,32 @@ def d12(F, K, sigma, T): d2 -= 0.5 * sigmaT return d1, d2 -@jit(float64(float64),cache=True,nopython=True) + +@jit(float64(float64), cache=True, nopython=True) def cnd_erf(d): + """ 2 * Phi where Phi is the cdf of a Normal """ RSQRT2 = 0.7071067811865475 return 1 + erf(RSQRT2 * d) -@jit(float64(float64,float64,float64,float64,boolean),cache=True,nopython=True) + +@jit(float64(float64, float64, float64, float64, boolean), cache=True, nopython=True) def black(F, K, T, sigma, payer=True): d1, d2 = d12(F, K, sigma, T) if payer: return 0.5 * (F * cnd_erf(d1) - K * cnd_erf(d2)) else: - return 0.5 * (K * cnd_erf(-d2) - F * cnd_erf(-d1)) + return 0.5 * (K * cnd_erf(-d2) - F * cnd_erf(-d1)) + -@jit(float64(float64,float64,float64,float64),cache=True,nopython=True) +@jit(float64(float64, float64, float64, float64), cache=True, nopython=True) def Nx(F, K, sigma, T): - return cnd_erf((log(F/K) - sigma**2 * T /2) / (sigma * sqrt(T))) /2 + return cnd_erf((log(F/K) - sigma**2 * T / 2) / (sigma * sqrt(T))) / 2 + def bachelier(F, K, T, sigma): """ Bachelier formula for normal dynamics need to multiply by discount factor """ - d1 = (F - K) / ( sigma * sqrt(T)) + d1 = (F - K) / (sigma * sqrt(T)) return (0.5 * (F - K) * cnd_erf(d1) + sigma * sqrt(T) * norm.pdf(d1)) |